Question

The time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation below. f (l) = 2 pi StartRoot StartFraction l Over 32 EndFraction EndRoot, where l is the length of the pendulum in feet What is the approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth?

Answer 1

the answer is d on edge 2020

Explanation:

Answer 2

46.08 feet.

Explanation:

Given that, for length,
`l` feet, the time period,
`f(l)`, of the pendulum is

`f(l)=2\pi\sqrt{(l)/(32)}`.

As the time period equals the time taken by the pendulum in one back and forth motion, so, actually, the given
`2.4\pi` seconds to swing back and forth is the time period.

Let
`l_0` feet be the length of the pendulum for the time period
`2.4\pi` seconds, so

`f(l_0)=2.4\pi`

`\Rightarrow 2\pi\sqrt{(l_0)/(32)}=2.4\pi`

`\Rightarrow \sqrt{(l_))/(32)}=1.2`

`\Rightarrow (l_0)/(32)=(1.2)^2` [squaring on both the sides]

`\Rightarrow l_0=1.44*32`

`\Rightarrow l_0=46.08`

Hence, the approximate length of a pendulum that takes
`2.4 \pi` seconds to swing back and forth is 46.08 feet.